Answer:
a) ![Z = 0.0085](https://tex.z-dn.net/?f=Z%20%3D%200.0085)
b) ![Z = 0.0095](https://tex.z-dn.net/?f=Z%20%3D%200.0095)
c) ii. Amy
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question a:
Nina took a test in English and earned a 71.8. In the English class had a mean of 71.7 and a standard deviation of 11.7.
This means that ![X = 71.8, \mu = 71.7, \sigma = 11.7](https://tex.z-dn.net/?f=X%20%3D%2071.8%2C%20%5Cmu%20%3D%2071.7%2C%20%5Csigma%20%3D%2011.7)
So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{71.8 - 71.7}{11.7}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B71.8%20-%2071.7%7D%7B11.7%7D)
![Z = 0.0085](https://tex.z-dn.net/?f=Z%20%3D%200.0085)
Question b:
Amy took a test in Social Studies and earned a 60.7. Students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5.
This means that ![X = 60.7, \mu = 60.6, \sigma = 10.5](https://tex.z-dn.net/?f=X%20%3D%2060.7%2C%20%5Cmu%20%3D%2060.6%2C%20%5Csigma%20%3D%2010.5)
So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{60.7 - 60.6}{10.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B60.7%20-%2060.6%7D%7B10.5%7D)
![Z = 0.0095](https://tex.z-dn.net/?f=Z%20%3D%200.0095)
c) Which person did relatively better?
Amy had a higher z-score, so she did relatively better.
Answer:
Pic1 answers:
P(blue) = 4/26,
P(yellow or green) = 14/26
P(purple) = 0.0%
P(red or green) = 18/26
P(not pink) = 26/26
P(not blue) = 22/26
Pic2 answers:
P(u) = 1/12
P(Vowel) = 6/12
P(a,b,c,d,e) = 4/12
P(Not A) = 10/12
P(vowel or consonant) = 12/12
P(not an m,s,t) = 9/12
Answer:
80 Percent
Step-by-step explanation:
Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent
Hopefully this helps - let me know if you have any questions!
Answer:
Horizontal
Step-by-step explanation:
Answer:
![f^{-1}(x)=\sqrt[3]{x}-1](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D-1)
Step-by-step explanation:
![f(x)=(x+1)^3\\\\y=(x+1)^3\\\\x=(y+1)^3\\\\\sqrt[3]{x}=y+1\\\\y=\sqrt[3]{x}-1\\ \\f^{-1}(x)=\sqrt[3]{x}-1](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B1%29%5E3%5C%5C%5C%5Cy%3D%28x%2B1%29%5E3%5C%5C%5C%5Cx%3D%28y%2B1%29%5E3%5C%5C%5C%5C%5Csqrt%5B3%5D%7Bx%7D%3Dy%2B1%5C%5C%5C%5Cy%3D%5Csqrt%5B3%5D%7Bx%7D-1%5C%5C%20%5C%5Cf%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D-1)
Graphing both inverses, they will be symmetrical about the line
.